Method and apparatus for measuring thickness of thin films via transient thermoreflectance

ABSTRACT

A method for measuring the thickness of a film is based on monitoring a transient change of the reflectivity of the film following an impulsive heating. The method includes the steps of impulsively irradiating a surface of the film with an excitation pulse to cause a rise in temperature in the film; irradiating the surface of the film with a probe beam, such that it reflects off the surface of the film to generate a reflected probe beam; detecting a time-dependent variation in intensity of the reflected probe beam; generating a signal waveform based on the measured variations in intensity; and determining the thickness of the film based on the signal waveform.

The invention relates to the field of optical metrology to determineproperties of a sample, e.g., a thin film.

Fabrication of microelectronic devices typically includes deposition andpatterning of multiple metal and dielectric layers. Optical techniquesof film thickness measurement are most suited for industrial processcontrol because they are typically fast, non-contact andnon-destructive. However, optical measurement of metal film thickness isa challenging problem because metal films are typically opaque.

An optical measurement called thermal wave detection has been usedpreviously to measure a variety of different material properties of asample, such as film thickness. In thermal wave detection measurements,a periodically modulated excitation beam heats a sample. Measuringintensity variations of a reflected probe beam monitors periodictemperature changes at the film surface. The magnitude and/or phase ofthe measured intensity variations are then used to determine propertiesof a sample. This method is shown, for example in U.S. Pat. No.5,978,074 entitled APPARATUS FOR EVALUATING METALIZED LAYERS ONSEMICONDUCTORS herein incorporated by reference. A similar methodutilizing a low modulation frequency and only measuring the magnitude ofthe probe beam intensity variations is described in U.S. Pat. No.6,054,868 entitled APPARATUS AND METHOD FOR MEASURING A PROPERTY OF ALAYER IN A MULTILAYERED STRUCTURE and incorporated herein by reference.

Another prior art optical technique called transient thermoreflectanceutilizes a short (typically, femtosecond or picosecond) excitation laserpulse to impulsively heat up the surface of a sample, while theintensity of reflected probe pulse is measured to monitor the surfacetemperature dynamics. The probe pulse (typically, also a femtosecond orpicosecond pulse) is delayed with respect to the excitation, and themeasurement is repeated many times with variable delay in order toobtain the time dependence of the reflectivity. This technique isdescribed e.g. in . C. A. Paddock and G. L. Eesley, “Transientthermoreflectance from thin metal films,” J. Appl. Phys. 60, 285 (1986).

U.S. Pat. No. 5,748,317, entitled APPARATUS AND METHOD FORCHARACTERIZING THIN FILM AND INTERFACES USING AN OPTICAL HEAT GENERATORAND DETECTOR, (the contents of which are herein incorporated byreference) proposes a method of measuring thermal properties of thefilm-substrate interface by analyzing transient thermoreflectancemeasurements. However, transient thermoreflectance technique has notbeen used for film thickness measurements. This is because, as it willbe shown below, the relevant time scale of the temperature dynamicssensitive to the film thickness is typically in the range of tens ofnanoseconds i.e., not accessible with a typical femtosecond apparatusused for transient thermoreflectance measurements. In one study,“Time-resolved thermoreflectivity of thin gold films and its dependenceon film thickness”, J. Hohlfeld, J. G. Müller, S.-S. Wellershoff and E.Matthias, it has been found that the transient thermoreflectivity ofthin gold films on the time scale of 10 ps is sensitive to the filmthickness. Measurement described by Hohlfeld et al. could, in principle,be used for film thickness measurements. However, such measurementsrequire a complicated femtosecond apparatus, and, as follows from FIG. 3of the paper by Hohlfeld et al., would only be applicable for filmsthinner than 300 nm.

Accordingly, it would be desirable to provide a method and apparatus forquickly and simply measuring the properties of a sample, such as filmthickness, that does not suffer from the prior art limitations.

The present invention meets the need for a simple method for filmthickness measurement that would allow fast and reproduciblemeasurements of metal films for semiconductor manufacturing processcontrol in one aspect. The method includes the steps of impulsivelyirradiating a surface of the film with an excitation pulse to cause arise in temperature in the film; irradiating the surface of the filmwith a probe beam, such that it reflects off the surface of the film togenerate a reflected probe beam; detecting a series of variations inintensity of the reflected probe beam; generating a signal waveformbased on the measured variations in intensity; and determining thethickness of the film based on the signal waveform.

In one embodiment of the invention, the step of irradiating the surfaceof the film with a probe beam is performed using continuous irradiation.In another embodiment of the invention, the step of irradiating thesurface of the film with a probe beam is performed usingquasi-continuous irradiation.

In another embodiment of the invention, the detecting step includesdetecting variations that form a time domain temperature response to theexcitation pulse.

In another embodiment of the invention, the determining step includesanalyzing the signal waveform with a mathematical model. In anotherembodiment, the mathematical model is derived based upon the opticalconstants of the film and thermal properties of the material ormaterials of which the film is comprised.

In still another embodiment, the determining step includes analyzing thesignal waveform with an empirical calibration. In another embodiment ofthe invention, the measuring and generating steps are performed by ahigh-speed detector and a transient digitizer, e.g. an oscilloscope.

In still another embodiment, the step of impulsively irradiating asurface of the film with an excitation pulse uses an excitation spotsize greater than 10 μm.

In another embodiment, the method measures a patterned metal/dielectricstructure with the feature size either larger or smaller than theexcitation or probe spot size.

In another embodiment, the method measures an isolated metal structureeither larger or smaller than a spot size of the excitation pulse.

In another aspect, the invention includes an apparatus for measuring thethickness of a film including a single irradiating means for irradiatinga single impulsive excitation beam to cause a rise in temperature in thefilm; irradiating means for irradiating the surface of the film with aprobe beam, such that it reflects off the surface of the film togenerate a reflected probe beam; a high speed photodetector fordetecting and measuring a series of variations in intensity of thereflected probe beam corresponding to variations in thermal decay withinthe surface of the thin film; an oscilloscope for generating a signalwaveform based on the measured variations in intensity; and amicrocomputer for determining the thickness of the film based on thesignal waveform.

In one embodiment, the irradiating means for irradiating a singleimpulsive excitation beam is a laser.

In another embodiment, the irradiating means for irradiating the surfaceof the film with a continuous probe beam is a laser.

The invention provides many advantages that are evident from thefollowing description, drawings, and claims.

The invention may be more completely understood in reference to thefollowing figures:

FIG. 1 depicts an apparatus for performing the method of measuring thinfilms according to the invention;

FIG. 2 depicts a chart of transient thermoreflectance signals obtainedfrom 500, 750, 1000, and 1500 angstroms thickness of TiN deposited on a1000 angstroms thick thermal oxide on silicon wafer; and

FIG. 3 depicts a chart showing effective decay time measured by fittingdata in FIG. 2 to an exponential function versus the film thickness.

FIG. 1 depicts an apparatus for carrying out the method of measuringthin film thickness according to the invention. In the proposed method,an excitation laser pulse 10, emitted by an excitation laser 1, with aduration of ˜1 ns or shorter, is incident onto a surface 15 of a metalfilm 11. Metal film 11 is deposited over a layer of dielectric 12 on asilicon wafer 13. Platform 100 supports waver 13. Absorption of theoptical radiation from laser pulse 10 at the surface 15 causes atemperature rise. This rise is followed by a decay caused by thermaldiffusion. As described below, the dynamics of this decay depends on thethickness of film 11. Qualitatively, the thicker the film, the longer ittakes to cool it down.

Probe laser beam 16, emitted by the probe laser 2, monitors thetemperature dynamics. The probe beam 16 overlaps the excitation beam 10at the sample surface 15. Probe beam 16 can be a continuous beam or aquasi-continuous beam. The latter term means a beam which is continuouson the time scale of a measurement i.e. typically from tens ofnanoseconds to microseconds. An example of a quasi-continuous beam wouldbe a beam modulated by rectangular pulses of 100 □s in duration. Theintensity of the reflected portion 17 of the probe beam 16 undergoesintensity variations corresponding to temperature variations at thesample surface. This is due to the dependence of the optical constantsof the film material on temperature. The reflected probe beam 17intensity is measured by a high-speed detector 18 connected tooscilloscope 19, with frequency bandwidth of ˜500 MHz or higher. Ifneeded, the detector 18 response can be averaged over multipleexcitation pulses 10. A computer 20 analyzes a signal waveform generatedby detector 18 and oscilloscope 19 to determine the thickness of thefilm 11.

Theoretical Estimates

The analysis below is based on a simple estimate for the length ofthermal diffusion for time t,L˜(χ^(t))^(1/2),  (1)where χ is the thermal diffusivity.

The fastest process happening upon the absorption of the excitationpulse 10 is the heat transfer across the film 11 thickness. According toequation (1), a characteristic thermal diffusion time through thethickness of the metal film h_(m) is given byτ₁˜h_(m) ²/χ_(m),  (2)where χ_(m) is the thermal diffusivity of the metal film. This time is˜10 ns for 1 □m-thick Cu film. For a 0.1 μm-thick Cu film, equation (1)yields τ₁˜1 ns. However, in this case, the classical thermal diffusionmodel is not valid because 0.1 μm is about the length of thenonequilibrium diffusion length for photoexcited electrons in Cu. Thisnonequilibrium diffusion is a very fast process taking less than 1 ps(see e.g. O. B. Wright and. V. E. Gusev, IEEE Trans. Ultrason. 42, 331(1995)). Thus for a Cu film of ˜0.1 □m or thinner, the thermalequlibrium across the film thickness is achieved almost instantaneouslycompared to the laser pulse duration of ˜0.5 ns.

After the thermal equlibrium across the film 11 thickness isestablished, the film 11 will cool down via two channels of heattransfer: lateral heat transport 111 within the plane of the film andvertical heat transfer 211 into the underlying dielectric 12. Accordingto equation (1), for lateral heat transport 111, the characteristicradius of the heat propagation R will be given byR˜a+(χ_(m) ^(t))^(1/2),  (3)

Where a is the excitation pulse 10 spot size. Due to the energyconservation requirement, the temperature should be inverselyproportional to the area over which the heat has diffused. Consequently,the temperature decay will be approximately described by $\begin{matrix}{{{{\left. {T(t)} \right.\sim\frac{a^{2}}{R^{2}}}T_{0}} = \frac{T_{0}}{1 + {2\frac{\sqrt{\chi_{m}t}}{a}} + \frac{\chi_{m}t}{a^{2}}}},} & (4)\end{matrix}$where T₀ is the initial temperature rise. The time needed for thetemperature to decay by a factor of two will be given byτ₂˜0.17a²/χ_(m),  (5)At t>>τ₂ the temperature will decay as 1/t.

For the vertical heat transport 211, first consider the case when thedielectric 12 is much thicker than the metal film 11. If L is the lengthof thermal diffusion into the dielectric 12, then conservation of energyleads to the following equation for the temperature decay:$\begin{matrix}{{{{\left. {T(t)} \right.\sim\frac{h_{m}\rho_{m}c_{m}}{{h_{m}\rho_{m}c_{m}} + {L\quad\rho_{d}c_{d}}}}T_{0}} = {\frac{1}{1 + \frac{\sqrt{\chi_{d}t}\rho_{d}c_{d}}{h_{m}\rho_{m}c_{m}}}T_{0}}},} & (6)\end{matrix}$where and ρ_(m,d) and c_(m,d) are the density and specific heat of metalfilm 11 and dielectric 12, respectively, and χ_(d) is the thermaldiffusivity of the dielectric 12. From equation (6), ½ decay time isfound to be:τ₃˜(ρ_(m)c_(m)h_(m))²/χ_(d)(ρ_(d)c_(d))².  (7)At large times t>>τ₃ the temperature will decay as t^(−1/2).

If the dielectric 12 thickness is much smaller compared to the metalfilm 11, the situation is different. Due to high thermal conductivity ofthe silicon substrate 13, the temperature rise at the dielectric12/silicon 13 interface can be assumed to be zero. The heat flow throughthe dielectric 12 is equal to the product of the thermal conductivity ofthe dielectric k_(d)=ρ_(d)c_(d)χ_(d) and temperature gradient across thedielectric layer 12, i.e. T/h_(d), where T is the temperature rise inthe metal film 11 and h_(d) is the dielectric 12 thickness. Temperaturedynamics of the metal film 11 is described by the equation$\begin{matrix}{{h_{m}\rho_{m}c_{m}\frac{\partial T}{\partial t}} = {{- \rho_{d}}c_{d}\chi_{d}\frac{T}{h_{d}}}} & (8)\end{matrix}$yielding an exponential thermal decay,T=T ₀exp(−t/τ ₃),  (9)with a decay time given byτ₃=(ρ_(m) c _(m) h _(m) h _(d))/(ρ_(d) c _(d)χ_(d)),  (10)

Note that in both cases τ₃ is highly sensitive to the metal 11 thicknesswhile τ₂ is independent of it. Therefore, the most favorable situationfor metal 11 thickness measurement via thermal decay is the one when thevertical heat transport 211 dominates i.e. τ₃<<τ₂. This can be achievedeither by using a large excitation spot (see an estimate below) or bymeasuring isolated test structures smaller than the excitation spotsize. If τ₂ and τ₃ are comparable, the measurement is possible but themathematical model used for signal analysis must take into account thelateral heat transport 111 and use the spot size as one of the modelparameters. Finally, if τ₃>>τ₂, the measurement will be insensitive tothe metal film 11 thickness.

As an example, quantitative estimates were performed for Cu films onthick silicon dioxide. According to equation (7), decay time τ₃ willvary between ˜50 ns and ˜5 μs as the film thickness increases from 0.1to 1 μm. The “lateral” decay time τ₂ will be of the order of 20 μs for a˜100 μm and ˜0.2 μs for a ˜10 μm. Thus the spot size of ˜10 μm will betoo small to measure a micron-thick film but still adequate for a ˜0.1μm-thick film, while ˜100 μm spot size will be adequate for an 1μm-thick film.

Experiment

For the experimental verification of the proposed method, the excitationwavelength was 532 nm, pulse energy about 1 μJ, pulse duration ˜0.5 ns,spot size 200×40 μm. The probe wavelength was 830 nm, spot size 30×15μm, and the probe power ˜1 μW. The small probe power led to a low signallevel and required averaging over 4800 laser shots. An increase of theprobe power to e.g. −1 mW will allow to obtain signals of similarquality with just a few laser shots, or increase the signal-to-noiseratio with more averaging.

Measurements were performed on TiN films which yielded goodthermoreflectance signals at the probe wavelength 830 nm. A shorterprobe wavelength would be better for measurements on copper.

Four samples with TiN films of thickness 500, 750, 1000 and 1500 Ådeposited on 1000 Å of thermal oxide on silicon wafers were used. FIG. 2depicts a chart showing the thermoreflectance transients obtained fromthe four samples. The horizontal axis of FIG. 2 corresponds to time inns, and the vertical axis of FIG. 2 corresponds to reflectivity changein arbitrary units. Curves 21, 22, 23, and 24 correspond to the sampleswith TiN thickness 500, 750, 1000 and 1500 Å, respectively. The negativesign of the signals indicates that reflectivity of TiN at 830 nmdecreases with temperature. As expected, the decay is slower for thickersamples. Note that two thicker samples 23, 24 yield a faster transientat the beginning of the signal. This can be ascribed to the relaxationacross the film thickness described by decay time τ₁, which, in thiscase, will be longer than the estimated time for Cu films because oflower thermal diffusivity of TiN.

FIG. 3 presents a chart showing the dependence of the effective thermaldecay time on the film 11 thickness. The horizontal axis of FIG. 3corresponds to TiN thickness in angstroms, and the vertical axis of FIG.3 corresponds to time in ns. The effective decay time was measured byfitting the signal waveforms to an exponential function within a timewindow from 15 to 50 ns. The points on the graph fall into a smoothcurve 31 which shows that the measurements are well suited for the filmthickness determination.

The preceding expressions and examples are exemplary and are notintended to limit the scope of the claims that follow.

1. A method for measuring the thickness of a film comprising:impulsively irradiating a surface of the film with an excitation pulseto cause a rise in temperature in the film; irradiating the surface ofthe film with a probe beam, such that it reflects off the surface of thefilm to generate a reflected probe beam; detecting a time-dependentvariation in intensity of the reflected probe beam; generating a signalwaveform based on the measured variation in intensity; determining thethickness of the film based on the signal waveform.
 2. The method ofclaim 1, wherein the step of irradiating the surface of the film with aprobe beam further comprises continuous irradiation.
 3. The method ofclaim 1, wherein the step of irradiating the surface of the film with aprobe beam further comprises quasi-continuous irradiation.
 4. The methodof claim 1, wherein the detecting step further comprises detectingvariations that comprises a time domain temperature response to theexcitation pulse.
 5. The method of claim 1, wherein the determining stepfurther comprises analyzing the signal waveform with a mathematicalmodel.
 6. The method of claim 5, wherein the mathematical model isderived based upon the optical constants of the film and thermalproperties of the material or materials of which compose the film. 7.The method of claim 1, wherein the determining step further comprisesanalyzing the signal waveform with an empirical calibration.
 8. Themethod of claim 1, wherein the measuring and generating steps areperformed by a high-speed detector and a transient digitizer such as anoscilloscope.
 9. The method of claim 1, wherein the step of impulsivelyirradiating a surface of the film with an excitation pulse furthercomprises an excitation spot size greater than 10 μm.
 10. The method ofclaim 1, where the method measures patterned metal/dielectric structureswith a feature size either larger or smaller than the excitation orprobe spot size.
 11. The method of claim 1, wherein the method measuresisolated test structures either larger or smaller than a spot size ofthe excitation pulse.
 12. An apparatus for measuring the thickness of afilm comprising: a single irradiating means for irradiating a singleimpulsive excitation beam to cause a rise in temperature in the film;irradiating means for irradiating the surface of the film with acontinuous probe beam, such that it reflects off the surface of the filmto generate a reflected probe beam; a high speed photodetector fordetecting and measuring a time-dependent variation in intensity of thereflected probe beam corresponding to the at the surface of the thinfilm; a transient digitizer such as an oscilloscope for generating asignal waveform based on the measured variations in intensity; acomputer for determining the thickness of the film based on the signalwaveform.
 13. The apparatus of claim 12, wherein the irradiating meansfor irradiating a single impulsive excitation beam further comprises alaser.
 14. The apparatus of claim 13, wherein said laser emits pulsesless than 10 ns in duration.
 15. The apparatus of claim 12, wherein theirradiating means for irradiating the surface of the film with a probebeam comprises a laser.
 16. The apparatus of claim 12, wherein the saidprobe beam is a continuous beam.
 17. The apparatus of claim 12, whereinthe said probe beam is a pulsed beam with the pulse duration longer than10 ns.